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Amy had $2400, which comprises of her school fee and her pocket money.

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kiran1213
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Amy had $2400, which comprises of her school fee and her pocket money. [#permalink] New post   Updated on: 24 Dec 2018, 21:45
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Amy had $2400, which comprises of her school fee and her pocket money. The amount was in denominations of $50, $100 and $500 notes. She gave 5 notes at her school fee counter. What is the minimum possible amount that she got as her pocket money if the number of $500 notes is greater than the number of $100 notes which in turn was less than the number of $50 notes?

A. $250
B. $300
C. $350
D. $400
E. None of these
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B

Originally posted by kiran1213 on 24 Dec 2018, 11:54.
Last edited by chetan2u on 24 Dec 2018, 21:45, edited 1 time in total.
Corrected the OA
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Re: Amy had $2400, which comprises of her school fee and her pocket money. [#permalink] New post   24 Dec 2018, 21:45
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kiran1213 wrote:
Amy had $2400, which comprises of her school fee and her pocket money. The amount was in denominations of $50, $100 and $500 notes. She gave 5 notes at her school fee counter. What is the minimum possible amount that she got as her pocket money if the number of $500 notes is greater than the number of $100 notes which in turn was less than the number of $50 notes?

A. $250
B. $300
C. $350
D. $400
E. None of these


We have to maximize the 500 notes to have minimum pocket money as these 500 notes would be part of 5 notes..
500 notes can be max 4...
Now let us distribute 400 $.. number of $50 is more than number of$100..
4*50 and 2*100 would give us 400..

Thus 4+4+2..
N(500)=N(50)>N(100)...

Let the five consist of 4*500+1*100=2100

Pocket money left is 2400-2100=300..
So Ans is B and not C..

Editing the OA
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Re: Amy had $2400, which comprises of her school fee and her pocket money. [#permalink] New post   25 Dec 2018, 10:42
kiran1213 wrote:
Amy had $2400, which comprises of her school fee and her pocket money. The amount was in denominations of $50, $100 and $500 notes. She gave 5 notes at her school fee counter. What is the minimum possible amount that she got as her pocket money if the number of $500 notes is greater than the number of $100 notes which in turn was less than the number of $50 notes?

A. $250
B. $300
C. $350
D. $400
E. None of these



given
50x+100y+500z=2400
and
z>y>x

she gave 5 notes
to get min amount left with her we need to find the max amount she would have given at counter

so 4*500+1*100= 2100
left with 2400-2100= 300
IMO B
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Re: Amy had $2400, which comprises of her school fee and her pocket money. [#permalink] New post   26 Jan 2020, 23:56
Let No. Of notes:
500-->x
100-->y
50 -->z
=>500x+100y+50z=2400
Or 10x+2y+z=48 where x,y,z are positive integers greater than 0.
Now,x can be max 4.
=> 2y+z=48-40=8
Similarly,y can be max 3 and therefore Zmax =2.
Now, we know that
School fee+Pocket money = 2400,
So to minimize Pocket money,we have to maximize School Fee.
Max school fee can be 500*4+100*1 as she has given 5 notes for school fee.
Therefore,pocket money can be 2*100+2*50 = 300.

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Re: Amy had $2400, which comprises of her school fee and her pocket money. [#permalink] New post   14 Jul 2021, 00:11
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We need a maximum of 500 denominations given at the fee counter to have minimum pocket money.

$50 = 6 notes
$500 = 4 notes
$100 = 1 notes

Total: 300 + 2000 + 100 = 2,400

For pocket money to be minimum, the fees paid should be higher. So, all 4 notes (500) and the remaining 1 should be of (100).

=> 2000 + 100 = 2,100

Pocket money = 2,400 - 2,100 = 300

Answer B
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Re: Amy had $2400, which comprises of her school fee and her pocket money. [#permalink]
14 Jul 2021, 00:11
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